ABSTRACT: The problems connected to propagation of a gravitational field are considered. The constant homogeneous gravitational field is investigated. The law of electromagnetic radiation frequency change in this gravitational field is shown. On the basis of the solution of the Einstein’s equation for a weak gravitational field, the flux of gravitational radiation energy from system of cooperating masses is found. The equation for gravitational waves is found. On the basis of refusal from a stresses tensor into energy-impulse tensor and use of a quantum gravitational eikonal, the quantum form of the energy-impulse tensor in Einstein’s equation is found. The equation for a graviton propagating in a gravitational field of a double star is found. Resonant interaction of a graviton and a gravitational field of a double star are investigated. It is shown that such interaction allows registering the gravitons.